Whole numbers are closed under addition because the sum of two whole numbers is always a whole number. explain how the process of checking polynomial division supports the fact that polynomials are closed under multiplication and addition.

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You have learned about the six trigonometric functions, their definitions, how to use them, and how to represent them graphically. the sine, cosine, and tangent trigonometric functions can be paired with their reciprocal functions, cosecant, secant, and cotangent, respectively. think about how each function is related to its reciprocal function. how are the graphs of the reciprocal functions related to their corresponding original functions? what happens to the graphs of the reciprocal functions as x approaches the zeros of the original functions? describe how you would teach friends with different learning styles (visual-spatial, aural-auditory, verbal-linguistic, physical-bodily-kinesthetic, logical-mathematical, social-interpersonal, and solitary-intrapersonal) how to graph the reciprocal functions

If you double the input of a function and it results in half the output, and if you triple the input and it results in a third of the output, what can be guessed about the function? check all that apply.